Soft value calculation for multilevel signals

ABSTRACT

A sub-optimal method is disclosed for calculating the reliability values (soft values) for the bits of a multilevel signal. The log-likelihood values are approximated using only the dominant terms, so called max-log approximation, that is for each bit position only the two closest signal symbols of opposite bit value (S 8 ,S 6 ) are considered in the sum. The used modulation scheme is 16-QAM together with Gray-labelling. Two versions of approximation are proposed: one version consists of using the two distances between the received value and the two closest symbols of opposite bit value (δ 1 , δ 2 ). In order to simplify and speed up the calculation, the second version consists of using the distance between the two closest symbols (δ 3 ) to approximate the distance between the second closest symbol and the received value. Furthermore, precalculated results are stored in look-up tables to speed up the calculation. Possible applications are especially bit interleaved coded modulation (BICM) together with soft-input decoding. It is also of interest for TCM and BCM schemes.

This invention relates to digital communications systems and, moreparticularly, the generation of soft reliability values for multilevelsignals.

Within the field of digital communications, multilevel modulation isused to map a number of bit sequences to a signal alphabet comprising anumber of signal symbols, i.e. a number of points in signal space. Forexample, a bit sequence may be mapped onto a point in a complex signalspace. A signal alphabet of size M allows log₂(M) bits to be mapped toeach symbol. However, when symbols are received at a receiver, they maybe affected by noise, thereby affecting the decoding of the signal whenretrieving the transmitted bit sequence. If multilevel modulation isused in conjunction with channel coding, many channel decoders, such asiterative decoders based on the BCJR algorithm, require so-called softbit values as an input. A soft bit value corresponds to a reliabilityvalue of a single bit being 0 or 1.

Examples of multilevel modulation include multi-amplitude levelmodulation in Pulse Amplitude Modulation (PAM), multi phase levelmodulation in Phase Shift Keying (PSK), multi signal point modulation inQuadrature Amplitude Modulation (QAM).

For example, an emerging technology for wideband digital radiocommunications of Internet, multimedia, video and othercapacity-demanding applications in connection with the third generationof mobile telephone systems is the evolving Wideband Code DivisionMultiple Access (WCDMA) specified as part of the 3GPP standardisationorganisation. Within this technology, High Speed Downlink Packet Access(HSDPA) is provided including a high speed downlink shared channel(HS-DSCH) which uses 16QAM. In 16QAM for example, M=16, i.e. each symbolin the signal alphabet represents 4 bits. Future releases may compriseeven larger constellation sizes such as 64 QAM.

It is known how to convert signal symbols to soft bit values bycalculating all distances in signal space between the received symboland all signal points of the signal alphabet. In particular, in order toobtain optimal performance, a likelihood ratio is calculated dependingon corresponding sums of probabilities where the probabilities arefunctions of the calculated distances. It is further known that in thecalculation of a likelihood ratio the sums of probabilities may beapproximated by the dominant contributions to the sums of probabilitiesin the likelihood ratio (A. J. Viterbi, “An intuitive justification anda simplified implementation of the MAP decoder for conventional codes”,IEEE Journal on selected areas in communications, 16(2), Feb. 1998).

Even though this approximation significantly reduces the computationalcomplexity while only causing a negligible loss in performance, acalculation of all distances to all the signal points is still requiredin order to determine which two are actually needed for the calculationof the likelihood ratio. For example, in a 16QAM modulation, 16distances have to be calculated for each received symbol. In particular,if a high rate of symbols needs to be decoded, e.g. several hundredsymbols per millisecond, the above performance issue is particularlysevere.

German patent no. DE 199 12 825 describes a method of receiving a datasymbol in which the closest constellation point of a corresponding 8-PSKmulti-symbol constellation is identified for a received data symbol.Subsequently, for each bit position, the symbol having a different valueat that position and which is closest to the Identified constellationpoint is looked up from a look-up table. A soft value is calculated asthe difference of the distances from the received symbol to the twoidentified constellation points. Hence, the number of distancecalculations is reduced.

It is an object of the invention to provide a method of generating areliability value that reduces the computational complexity.

The above and other problems are solved when a method of generating areliability value for a received multilevel signal in relation to anumber of predetermined signal symbols each associated with acorresponding bit sequence including a first bit position; thereliability value being indicative of likelihood information ofreceiving said multilevel signal comprises the steps of

-   -   identifying a first one of the number of signal symbols as being        closest to the received multilevel signal; and    -   estimating the reliability value based on a stored pre-computed        distance function of at least the first signal symbol and a        second one of the number of signal symbols, where the second        signal symbol is the signal symbol closest to the first signal        symbol of the signal symbols corresponding to a different binary        value at the first bit position of the respective associated bit        sequence than the first signal symbol.

Given a signal constellation, for each signal symbol and for each bitposition it is known which one of the other signal symbols having anopposite value at that bit position is closest to that signal symbol.Based on this information, a distance function of the signal symbol andthe closest signal symbol with opposite bit position may bepre-calculated and stored in a look-up table. Here, the termpre-computed distance function comprises any intermediate result of thecomputation of the reliability value from the first and second signalsymbol.

It has been realised by the inventors that the calculation of thereliability values may be based on a pre-computed distance functionwhere the function is pre-computed given the first signal symbol and asecond signal symbol, i.e. a pre-computed function of the first and thesecond signal symbol. The second signal symbol is the signal symbol thatis closest to the first signal symbol of all signal symbols of thenumber of signal symbols that have a different binary value at the firstbit position of the respective associated bit sequence than the firstsignal symbol. Hence, the complexity of the calculations to be performedupon receipt of a signal symbol is considerably reduced. Hence, theabove method is particularly well-suited for low-complexityimplementations in mobile receivers, as it reduces the requiredcomputational resources.

It is a further advantage that the closest signal point needed forcalculating the likelihood ratio is determined first, such that only thecorresponding distances to the identified signal points need to bedetermined. In this way, the computational complexity is reducedsignificantly, since not more than two distances need to be calculatedin order to determine the likelihood ratio for each bit.

According to a preferred embodiment of the invention, the storedpre-computed distance function comprises the distance between the firstsignal symbol and the second signal symbol, and the step of estimatingthe reliability value further comprises the step of determining a firstdistance between the received signal and the first signal symbol. Hence,the actual distance between the first and the second symbol ispre-calculated and stored. Once the first signal symbol is identified,this stored distance may be looked up and used as an approximation forthe distance between the received signal and the second signal symbol.Consequently, a further reduction in computational complexity isachieved, since only one distance has to be calculated.

When the step of estimating the reliability value comprises the step ofdetermining a polynomial function of the first distance and the seconddistance between the first signal symbol and the second signal symbol,multiplied by a predetermined constant, the computational complexity isfurther reduced, as no logarithm needs to be calculated. In oneembodiment, the polynomial function is a difference of the squareddistances.

According to yet another preferred embodiment of the invention, thestored pre-computed distance function is indicative of one of a numberof functional relations between the received multilevel signal and thereliability value, and the step of estimating the reliability valuefurther comprises the step of selecting a functional relation of saidnumber of functional relations dependant on the first signal symbol andthe first bit position. Hence, the calculation of the likelihood valueonly comprises the step of calculating the corresponding storedfunction. Preferably, the functional relationship is a linear functionof a signal component, thereby reducing the calculation to amultiplication operation and an adding operation.

According to yet another preferred embodiment, the stored pre-computeddistance function comprises, for each signal symbol and bit position, anapproximation of the corresponding reliability value. Hence, accordingto this embodiment, an approximation of the reliability value may bedirectly looked up once the closest signal symbol is identified, therebyproviding a computationally very efficient method which eliminates theneed of online distance calculations.

Preferably, the stored information is stored in a look-up tablecomprising a plurality of pre-computed distance functions indexed by thenumber of signal symbols and the bit positions of the number of bitsequences, thereby providing fast access to the information.

In one embodiment of the invention, the method further comprises thestep of providing the reliability value as an input to a decoder, e.g.an iterative decoder using the BCJR algorithm or any other decoder usingsoft values as an input. It is an advantage of the invention that itprovides an accurate and resource-efficient approximation of soft valuesas an input to such decoders.

The first signal symbol may be identified by comparing the signalcomponents with predetermined thresholds or decision boundaries, forinstance by means of a slicer, i.e. a circuit which compares a signalwith predetermined thresholds. Hence, a fast and computationallyinexpensive method is provided for identifying the closest signal symbolwithout the necessity of calculating all distances between the receivedvalue and all signal symbols.

It is a further advantage of the invention that cost-effective, standardcomponents may be employed when implementing a method according to theinvention.

When the likelihood information comprises a log-likelihood ratio, a highperformance quality Is achieved, as the use of a log-likelihoodcorresponds a theoretically optimal way of calculating soft reliabilityvalues. However, other methods of calculating likelihood information maybe employed, such as a log-likelihood of the signal power.

In a preferred embodiment of the invention the step of identifying thefirst signal symbol as being closest to the received multilevel signalcomprises the step of identifying the first signal symbol as beingclosest to the received multilevel signal with respect to a Euclideandistance measure in a signal space, as the Euclidean distance isdirectly related to the probabilities of a likelihood calculation.Alternatively, other suitable known metrics may be used insteadEuclidean distances.

The signal space may be a real or complex signal space. For example, inQAM modulation two amplitude-modulated signals are transmitted on asingle carrier, but shifted in phase by 90 degrees. Hence, the resultingsignal points may be represented in the complex plane representing theso-called in-phase (I) and quadrature (Q) components of the QAM signal.In general, in M-QAM, the corresponding signal constellation comprises Msignal symbols, where M=2^(n), n=2, 3, 4, 5, 6, 7, etc.

When the number of signal symbols is associated with the number of bitsequences such that the bit sequences associated with all nearestneighbours of each signal symbol only differ from the bit sequence ofthat signal symbol at one bit position, the error rate of thetransmission system is reduced. This form of mapping is referred to asGray mapping.

The invention further relates to an arrangement for generating areliability value for a received multilevel signal in relation to anumber of predetermined signal symbols each associated with acorresponding bit sequence including a first bit position; thereliability value being indicative of likelihood information ofreceiving said multilevel signal; characterised in that the arrangementcomprises

-   -   first processing means adapted to identify a first one of the        number of signal symbols as being closest to the received        multilevel signal;    -   storage means adapted to store information related to the first        signal symbol and a second one of the number of signal symbols        being closest to the first signal symbol and corresponding to a        different binary value at the first bit position of the        respective associated bit sequence than the first signal symbol;        and    -   second processing means adapted to estimate the reliability        value on the basis of the stored information.

The arrangement may be implemented by any processing unit, e.g. aprogrammable microprocessor, an application-specific integrated circuit,or another integrated circuit, a smart card, or the like. The termprocessing means comprises general- or special-purpose programmablemicroprocessors, Digital Signal Processors (DSP), Application SpecificIntegrated Circuits (ASIC), Programmable Logic Arrays (PLA), FieldProgrammable Gate Arrays (FPGA), etc., or a combination thereof. Theprocessing means may be a CPU of a computer, a microprocessor, a smartcard, a SIM card, or the like. The first and second processing means maybe separate processing means, e.g. separate circuits, or they may becombined in one processing means, e.g. performed by suitableinstructions executed by a programmable microprocessor.

The term storage means includes magnetic tape, optical disc, digitalvideo disk (DVD), compact disc (CD or CD-ROM), mini-disc, hard disk,floppy disk, ferro-electric memory, electrically erasable programmableread only memory (EEPROM), flash memory, EPROM, read only memory (ROM),static random access memory (SRAM), dynamic random access memory (DRAM),synchronous dynamic random access memory (SDRAM), ferromagnetic memory,optical storage, charge coupled devices, smart cards, etc.

Furthermore, the above discussed features and steps of the methodaccording to the invention may be incorporated in the above arrangementaccording to the invention.

The invention further relates to a device for receiving multilevelsignals comprising an arrangement as described above and in thefollowing.

The device may be any electronic equipment or part of such electronicequipment, where the term electronic equipment includes computers, suchas stationary and portable PCs, stationary and portable radiocommunications equipment. The term portable radio communicationsequipment includes mobile radio terminals such as mobile telephones,pagers, communicators, e.g. electronic organisers, smart phones, PDAs,or the like.

The invention will be explained more fully below in connection withpreferred embodiments and with reference to the drawings, in which:

FIGS. 1 a-b schematically show a receiver according to an embodiment ofthe invention;

FIG. 2 shows an example of a signal constellation with 16 signalsymbols;

FIG. 3 shows a flow diagram of a method of determining reliabilityvalues;

FIG. 4 shows an example of a look-up table for use in the method of FIG.3;

FIG. 5 shows a flow diagram of a method according to an embodiment ofthe invention;

FIG. 6 shows an example of a look-up table according to the embodimentof FIG. 5;

FIG. 7 shows another example of a signal constellation with 16 signalsymbols;

FIG. 8 shows a flow diagram of a method according to another embodimentof the invention; and

FIG. 9 shows an example of a look-up table according to the embodimentof FIG. 8.

FIG. 1 a schematically shows a receiver according to an embodiment ofthe invention receiving a radio signal from a transmitter via acommunications channel. Transmitter 101 is adapted to send a signal svia a noisy channel 102 to receiver 103. The signal s represents one ofa set of M signal points S₁ . . . S_(M) in a signal space where eachsignal point is related to a respective bit sequence of log₂(M) bits. Inthe presence of noise in the transmission channel 102, the receiver 103receives a signal r′ that deviates from the transmitted signal s. In oneembodiment the signal is a Code Division Multiple Access (CDMA) signalusing a spread spectrum technique. The receiver 103 comprises a receivercircuit 107 for transforming the received spread spectrum signal intothe signal symbol r. The receiver further comprises a channel decoder106 for decoding the received signal symbol r, e.g. a BCJR or Viterbidecoder. The decoder 106 requires soft bit values as an input. Hence,the receiver 103 further comprises a circuit 104 which is adapted tocalculate soft values for the log₂(M) bits of the received signal symbolr and to provide the calculated soft values to the decoder 106.According to the invention, the receiver 103 further comprises a memory105, such as on-chip memory, EPROM, flash memory, or the like, in whicha look-up table is stored for use in an efficient calculation of thesoft values by the circuit 104, preferably as described in connectionwith FIGS. 3-9.

FIG. 1 b schematically shows a more detailed block diagram of thereceiver circuit 103 of fig. The circuit 107 comprises a RAKE receiver110 suitable for receiving CDMA signals, i.e. a receiver which usesseveral baseband correlators to individually process several signalmultipath components. The correlator outputs are combined to achieveimproved communications reliability and performance (see e.g. “DigitalCommunications” 4th Edition, by John G. Proakis, McGraw-Hill, 2000). Thesampled received radio signal r′ is fed to the RAKE receiver 110 whichgenerates the signal symbol r to be decoded. The circuit 107 furthercomprises a channel estimator 111 and a noise estimator 112, e.g.implementing any suitable channel estimation and noise estimationtechnique known in the art. The channel estimator receives the receivedradio signal r, identifies up to N different radio paths or channel tapsand estimates corresponding delays Δ_(k), k=1, . . . ,N, and complexchannel estimate h_(r)=(h_(r1), . . . h_(rN)) of these paths. Thechannel estimator 111 further provides a set of complex combiner weightsw=[w₁w₂ . . . w_(N)]^(T) to be used by the rake receiver. Here,

^(T) denotes a transposed vector. For example, the weights may bedetermined according to an optimisation criterion, such as maximisingthe received signal energy.

The calculated delays Δ_(k) and the combiner weights are provided to therake receiver 110. The RAKE receiver 110 comprises delay circuits 115which delay the incoming signal according to the N channel taps.Further, the receiver 110 comprises circuitry 116 for multiplying the Ndelayed versions of the received signal with a spreading code c fordispreading the spread spectrum signals and circuitry 117 for summingthe signals to form a radio symbol. Furthermore, the rake receiver 110comprises multiplier circuitry 118 for multiplying each of the N radiosymbols with the combiner weights (w_(k))*, k=1, . . . ,N, where ( )*denotes complex conjugation. Finally, the RAKE receiver 110 comprises anadding circuit 119 which combines the weighted symbols to form thereceived symbol estimate r which is fed to the soft value calculationcircuit 104.

When using a multilevel constellation of signal points S₁ . . . S_(M)the amplitude information should be maintained in order to ensuresuccessful demodulation in the receiver. Consequently, the referencepoints S₁ . . . S_(M) should be scaled properly. In the following it Isassumed that the channel estimator 111 estimates the channel gain on thebasis of a reference channel hr which has a channel gain that may bedifferent from the actual gain of the traffic channel, e.g. a HS-DSCH.The gain difference between the reference channel and the trafficchannel may be denoted with g. Hence, the received symbol r after theRAKE receiver 110 may be expressed asr=gW ^(H) h _(r) s+n,where w^(H) is the Hermitian conjugate of w, w^(H)h_(r) denotes an innerproduct, s is the transmitted symbol and n is a noise term, e.g.representing additive white Gaussian noise (AWGN). The gain parameter gis signalled to the receiver, w is selected by the combiner in thereceiver, and h_(r) are the channel estimates. Hence, at the receiver,the reference signal symbols S₁ . . . S_(M) may be scaled appropriately,according toŜ _(j) =gw ^(H) h _(r) S _(j), j=1, . . . ,M.  (0)

In FIG. 1 b, the receiver circuit 107 comprises circuit 113 adapted tocalculate the above scaling factor gw^(H)h_(r) and a multiplier circuit114 for multiplying the reference symbols with the scaling factor,resulting in properly scaled signal symbols Ŝ₁, . . . ,Ŝ_(M), which arefed into the soft value calculation circuit 104.

Finally, the noise estimator 112 provides an estimate of the signalnoise level σ which is fed into the soft value calculation circuit 104.

According to the invention, the soft value calculation circuit locatesthe signal symbol which is closest to the received signal r andcalculates corresponding soft values L_(m) for bit m, m=1, . . .,log₂(M), e.g. according to one of the embodiments discussed inconnection with FIGS. 3-9.

It is noted that the receiver circuit described in connection with FIGS.1 a-b merely serves as an example, and the scope of the invention is notlimited to the type of receiver, nor to the above scaling of signalsymbols.

FIG. 2 shows a signal constellation with 16 signal symbols. The signalconstellation comprises M=16 signal points S₁ through S₁₆ in atwo-dimensional signal space, e.g. the I/Q components in a 16QAM signalconstellation. Preferably, the signal points are distributed regularly,such that the distance to the nearest neighbours of each signal point isthe same. The reference points may take values that suit theimplementation in question. However, alternatively, other signalconstellations may be chosen. In FIG. 2, 16 different bit sequences 0000through 1111, each consisting of log₂(M)=4 bits, are mapped onto thesignal points S₁-S₁₆. Preferably, the mapping of the bit sequences tothe signal points is chosen such that the bit sequence of each signalpoint only differs from those of the nearest neighbours by one bit,thereby optimising the decoding performance. For example, in FIG. 2,signal point S₈ has three nearest neighbours, S₄, S₇, and S₁₂. The bitsequence of S₄, i.e. 1111, differs from the sequence 1110 of S₈ only atbit position 4, etc. Alternatively, other mappings may be chosen.

For every bit position m mapped on a signal point, the signal points inthe constellation may be divided into two sets where the signal pointsin each set have bit value 0 and 1, respectively, at that position. Inthe following, the set of signal points with a 0 at the m-th position isdenoted A_(0,m), and the corresponding set with a 1 at the m-th positionis denoted A_(1,m). For example, in the example of FIG. 2 and for m=1,A_(1,1)={S₃, S₄, S₇, S₈, S₁₁, S₁₂, S₁₅, S₁₆} and A_(0,1)={S₁, S₂, S₅,S₆, S₉, S₁₀, S₁₃, S₁₄}. The sets are of equal size with M/2 elementseach.

When one of the signals S₁, . . . ,S₁₆ is transmitted over a noisychannel, the received signal will differ from the transmitted signalaccording to a corresponding distribution. The actual shape and width ofthe distribution of received signals depends on the characteristics ofthe noise. In FIG. 2, the cross 201 represents an example of a receivedsignal r.

Prior to providing the received 16QAM radio symbols to a decoder, e.g. aturbo decoder, they are converted into soft values. Hence, a soft valueis calculated for each bit of every 16QAM symbol. A soft value of them-th bit in the sequence mapped to r may be defined as $\begin{matrix}\begin{matrix}{L_{m} = {\log\quad\frac{P\left( {s_{m} = \left. 1 \middle| r \right.} \right)}{P\left( {s_{m} = \left. 0 \middle| r \right.} \right)}}} \\{= {\log\quad\frac{{P\left( {s_{m} = 1} \right)}\quad{P\left( {\left. r \middle| s_{m} \right. = 1} \right)}}{{P\left( {s_{m} = 0} \right)}\quad{P\left( {\left. r \middle| s_{m} \right. = 0} \right)}}}} \\{= {\log\quad\frac{P\left( {\left. r \middle| s_{m} \right. = 1} \right)}{P\left( {\left. r \middle| s_{m} \right. = 0} \right)}}}\end{matrix} & (1)\end{matrix}$where s_(m) is the m-th bit in the bit sequence represented by thetransmitted signal, and P(s_(m)=i| r), i=0,1, are the a posterioriprobabilities of the bit s_(m) where r is the received signal. It isnoted that the second equality assumes that s_(m)=1 and s_(m)=0 areequally probable in the chosen alphabet. Otherwise, the overall ratio ofprobabilities should be taken into consideration in the following.However, this would only give rise to a constant factor. Hence, L_(m)corresponds to a log-likelihood ratio of probabilities. Theprobabilities P(r|s_(m)=i) in eqn. (1) may be written as $\begin{matrix}\begin{matrix}{{{P\left( {\left. r \middle| s_{m} \right. = i} \right)} = {\frac{2}{M}\quad{\sum\limits_{s \in A_{i,m}}{P\left( {r,s} \right)}}}},} & {{i = 0},1.}\end{matrix} & (2)\end{matrix}$Hence, the calculation of the above probability involves a summationover M/2 terms each including a joint probability P(r,s). This is acomputationally expensive task, especially if M is large, e.g. M=64.

In many applications, the above soft values L_(m) may be approximated by$\begin{matrix}\begin{matrix}{L_{m} = {\log\quad\frac{\max\limits_{s \in A_{1,m}}{P\left( {r,s} \right)}}{\max\limits_{s \in A_{0,m}}{P\left( {r,s} \right)}}}} \\{\quad{{= {\log\quad\frac{P\left( r \middle| {\hat{s}}_{1,m} \right)}{P\left( r \middle| {\hat{s}}_{0,m} \right)}}},}}\end{matrix} & (3)\end{matrix}$where ŝ_(l,m), i=0,1, are the signal points that result in the largestcontribution to the sums in eqn. (2). Hence, in the calculation of theprobabilities, the sums over M/2 terms are approximated by the theirrespective dominant terms, according to $\begin{matrix}{{\log\quad{\sum\limits_{s \in A_{i,m}}{P\left( {r,s} \right)}}} \approx {\log\quad{\max\limits_{s \in A_{i,m}}{{P\left( {r,s} \right)}.}}}} & (4)\end{matrix}$The above approximation is often referred to as the “max log MAP”approximation which yields a good approximation in cases where the abovesums are dominated by one term, as for example in the case of Gaussiannoise when the signal to noise ratio (SNR) is large. The aboveprobabilities depend on the distances between the received signal r andthe respective signal points. For example, in the case of additivezero-mean Gaussian noise with variance σ², the log-likelihood ratio ofeqn. (3) may be expanded as $\begin{matrix}\begin{matrix}{L_{m} = {\log\quad\frac{\sigma^{- 2}\quad{\exp\left( {{- {{r - {\hat{s}}_{1,m}}}^{2}}/\sigma^{2}} \right)}}{\sigma^{- 2}\quad{\exp\left( {{- {{r - {\hat{s}}_{0,m}}}^{2}}/\sigma^{2}} \right)}}}} \\{= {{\sigma^{- 2}\left( {{{r - {\hat{s}}_{0,m}}}^{2} - {{r - {\hat{s}}_{1,m}}}^{2}} \right)}.}}\end{matrix} & (5)\end{matrix}$

It is noted that it is assumed that the ŝ_(l,m) are scaled correspondingto the received signal according to equation (0) above. In thefollowing, we define d_(l,m)=|r−ŝ_(l,m)|, for i=0,1, to be the distancesbetween the received signal r and the closest signal points in the setsA_(l,m), respectively. For example, in FIG. 2, for m=1, d_(0,1)corresponds to the distance δ₂ between r and the closest signal point inA_(0,1), i.e. S₆, while d_(1,1), corresponds to the distance δ₁ betweenr and the closest signal point in A_(1,1), i.e. S₈. According to theinvention, the likelihood ratio in equation (5) is obtained by firstidentifying the closest signal point S₈, and then determining thedistances δ₁ and δ₂, as will be described in greater detail below.Hence, a computationally expensive calculation of all the distancesbetween r and all the signal points S₁ . . . S₁₆ in order to identifythe shortest distances δ₁ and δ₂ is avoided. Alternatively toidentifying S₆ by means of a look-up table and then calculating δ₂, thedistance δ₃ between S₆ and S₈ is looked up and used as an approximationinstead of δ₂, thereby saving additional computational resources. Thiswill be described in greater detail in connection with FIGS. 5-6. Afurther embodiment of the invention will be described in connection withFIGS. 8-9.

It is noted that, preferably, in the above estimation of the reliabilityvalues, a proper scaling of the signal points in the QAM constellationis taken into consideration. If this scaling is taken intoconsideration, the above log-likelihood ratio may be written asL _(m)=σ⁻²·(|r−ŝ _(0,m)|² −|r−ŝ _(1,m)|²).  (6)

As described in connection with FIG. 1 b, when using a multilevelconstellation as in the example of FIG. 2, the amplitude informationshould be maintained in order to ensure successful demodulation in thereceiver. Consequently, the reference points S_(j), j=1, . . . ,16should be scaled properly. If this scaling is taken into consideration,the above log-likelihood ratio may be written asL _(m) =K·(|{tilde over (r)}−{tilde over (s)}_(0,m)|²−|{tilde over(r)}−{tilde over (s)}_(1,m)|²),  (7)i.e. with the properly scaled signals $\begin{matrix}\begin{matrix}{\overset{\sim}{r} = \frac{r}{g\quad w^{H}h_{r}}} \\\begin{matrix}{{\overset{\sim}{s}}_{i,m} = \frac{{\hat{s}}_{i,m}}{g\quad w^{H}h_{r}}} & \quad & {{m = 1},\ldots\quad,{\log_{2}(M)},} & {{i = 0},1,}\end{matrix}\end{matrix} & (8)\end{matrix}$and whereK=(gw ^(H) h _(r))²/σ²  (9)is a constant which depends on the signal to noise ratio.

FIG. 3 shows a flow diagram of a method of determining reliabilityvalues. According to this method, the soft values L_(m) are calculatedusing the approximation in equation (7). Initially, in step 301, asignal r is received and, in step 302, the signal point {haeck over (s)}from the set of signal points S₁ . . . S_(M) which, according to aEuclidean metric, is closest to r is identified. For example, anefficient way of identifying {haeck over (s)} is by means of a slicer.In step 303, the distance δ₁ between r and {haeck over (s)} iscalculated. Subsequently, for bit positions m=1, . . . ,log₂(M), thefollowing steps are performed: In step 304, the signal point ŝ which isclosest to {haeck over (s)} is looked up in a look-up table 308. Thissignal point corresponds to the signal point which is closest to r andhas the opposite bit value at position m than {haeck over (s)}. In step305, the distance δ₂ between r and ŝ is calculated. Based on thedistances δ₁ and δ₂, the soft value L_(m) is now approximated accordingto eqn. (7) above: If the bit value ŝ_(m) of ŝ at position m is 0, thesoft value is approximated by L_(m)=K (δ₂)²−(δ₁)² (step 306). Otherwisethe soft value is approximated by L_(m)=K (δ₂)²−(δ₁)² (step 307). Here,K is a constant which depends on the noise distribution as describedabove. Referring to the example illustrated in FIG. 2, the closestsignal point to the received signal r (marked by the cross 201) is{haeck over (s)}=S₈. When calculating a soft value L₁ for the first bitposition m=1 using the method of FIG. 3, the first bit in S₈ isidentified to be {haeck over (s)}₁=1. From a pre-computed look-up table,e.g. as illustrated in FIG. 4, the closest signal point with a “0” inthe first bit position is ŝ=S₆. Hence, the distances δ₁ and δ₂ may becalculated as δ₁=|r−S₈| and δ₂=|r−S₆|, respectively, where | | denotesthe Euclidean distance. Thus, the soft value L₁ is approximated byL₁=K(δ₂)²−(δ₁)².

Consequently, the method described above requires at the most 1+log₂(M)distance calculations, since the closest distance 8 j has to becalculated once for a received signal (step 303) and, for each bitposition m, the distance 82 is calculated in step 305. This is to becompared with M distance calculations when all distances to all signalpoints are calculated. Hence, the computational complexity of thismethod only grows logarithmically with the size of the symbol alphabetrather than proportional to the alphabet size. This is a considerablereduction of the computational complexity, in particular for largealphabet sizes.

FIG. 4 shows an example of a look-up table for use with the method ofFIG. 3. The look-up table 308 identifies the pre-computed closest signalpoints and is indexed by the bit numbers m and the signal points S₁ . .. S_(M). Each row corresponds to one of the signal points S₁ . . .S_(M). For example, row 402 corresponds to signal point S₂, such thateach element in row 402 identifies a signal point which is the closestto S₂ among all signal points having a bit value opposite to S₂ at bitposition m. Each entry in table 308 consumes log₂(M) bits foridentifying one out of M signal points. Furthermore, the table consistsof M rows and log₂(M) columns. Consequently, the table requires M[log₂(M)]² bits. For example for M=8 the memory consumption is 72 bitsand for M=16 the memory consumption is 256 bits.

FIG. 5 shows a flow diagram of a method according to an embodiment ofthe invention. Again, this embodiment utilises the approximation ofequation (7) for the calculation of the soft values L_(m). As in themethod of FIG. 3, in the initial step 501, a signal r is received and,in step 502, the signal point {haeck over (s)} from the set of signalpoints S₁ . . . S_(M), which is closest to r is identified, e.g. bymeans of a slicer. In step 503, the distance δ₁ between r and {haeckover (s)} is calculated. Subsequently, for bit positions m=1, . . .,log₂(M), the following steps are performed: In step 504, the distanceδ₃ between {haeck over (s)} and the signal point ŝ which is closest to{haeck over (s)} and has the opposite bit value at position m is lookedup in a look-up table 508. Subsequently, this distance δ₃ is used as anapproximation for the distance δ₂ between r and ŝ when approximating thesoft value L_(m) according to eqn. (7) above. Hence, if the bit valueŝ_(m) of ŝ at position m is 0, the soft value is approximated by L_(m)=K(δ₃)²−(δ₁)² (step 506). Otherwise the soft value is approximated byL_(m)=K (δ₁)²−(δ₃)² (step 507). Again, K is a constant which depends onthe noise distribution. Referring again to the example illustrated inFIG. 2, the closest signal point to the received signal r is {haeck over(s)}=S₈. When calculating a soft value L₁ for the first bit position m=1using the method of FIG. 5, the first bit in S₈ is identified to be{haeck over (s)}₁=1. From a pre-computed look-up table, e.g. asillustrated in FIG. 6, the distance to the closest signal point with a“0” in the first bit position is d_(1,8)=δ₃. Hence, the distance δ₁ iscalculated as δ₁=|r−S₈| and δ₂ is approximated by δ₃. Thus, the softvalue L₁ is approximated by L₁=K (δ₃)²−(δ₁)².

Consequently, as the pre-computed distance δ₃ is used as anapproximation for δ₂, the method according to this embodiment requiresonly one distance calculation, i.e. the calculation of δ₁ (step 503).Again, this is to be compared with M distance calculations when alldistances to all signal points are calculated.

Hence, it is an advantage of this embodiment that the computationalcomplexity does not grow with the size of the symbol alphabet, therebyyielding a computationally efficient method of approximating softvalues.

Hence, it is an advantage that storing the look-up table only requireslittle storage space.

It is a further advantage of the method according to the invention, thatit yields a good approximation of the soft values, thereby providing agood decoding performance.

FIG. 6 shows an example of a look-up table according to the embodimentof FIG. 5. The look-up table 508 comprises the pre-computed distancesbetween the signal points in a constellation of size M. A distanced_(m,k) in table 508 denotes the Euclidean distance between signal pointS_(k) and the closest signal point with opposite bit value at positionm. Assuming that each distance is stored with a resolution requiring Tbits, each entry in the table 508 requires η bits. Furthermore, thetable consists of M rows and log₂(M) columns. Consequently, the tablerequires η M log₂(M) bits. For example, for M=8 the memory consumptionis 24η bits and for M=16 the memory consumption is 64η bits. Hence, itis a further advantage of this embodiment that it requires littlestorage capacity. In an embodiment where the resolution of thepre-computed distances is higher than log₂(M) bits, i.e. η>log₂(M),processing time is traded for memory space in comparison with the methodof FIGS. 3-4.

It is noted that additional storage space may be saved by only storingeach distance once, i.e. in case the same distance appears in two ormore entries of the table, a reference to that distance may be stored inone of the entries, instead.

Alternatively, other layouts of a look-up table may be used. Forexample, in one embodiment, the look-up table may comprise all M(M−1)/2mutual distances between the signal points S_(k), thus requiringηM(M−1)/2 bits of storage. However, for M>4 this embodiment requireslarger storage capacity than the embodiment of FIG. 6.

FIG. 7 shows another example of a signal constellation with 16 signalsymbols. As in FIG. 2, the signal constellation comprises M=16 signalpoints S₁ through S₁₆ in a two-dimensional signal space, e.g. the I/Qcomponents in a 16QAM signal constellation. The signal points aredistributed regularly, such that the distance to the nearest neighboursof each signal point is the same. In the example of FIG. 7, they areassumed to be selected such thatS _(k) =x _(k) +jy _(k), where x_(k), y_(k)ε[−3d, −d, d, 3d], k=1, . . .,M,where d is an arbitrary constant and where j²=−1. For example, d may bechosen to d=1. However, alternatively, other signal constellations maybe chosen.

In FIG. 7, 16 different bit sequences 0000 through 1111, each consistingof log₂(16)=4 bits, are mapped onto the signal points S₁, . . . ,S₁₆.Preferably, the mapping of the bit sequences to the signal points ischosen to be a Gray mapping, i.e. such that the bit sequence of eachsignal point only differs from those of the nearest neighbours by onebit, thereby optimising the decoding performance.

As above, for every bit position m mapped on a signal point, the signalpoints in the constellation may be divided into two sets A_(0,m) andA_(1,m,) where the signal points in each set have bit value 0 and 1,respectively, at that position.

FIG. 8 shows a flow diagram of a method according to another embodimentof the invention. Again, this embodiment utilises the approximation ofequation (7) for the calculation of the soft values Lm. As in theembodiment of FIG. 3, in the initial step 801, a signal r is received.The received signal may be written as r=Re(r)+jlm(r) and, in thefollowing the magnitude of the I- and Q components of r will be denotedby a=|Re(r)| and b=|lm(r)|, respectively. After the received symbol iscombined in the combiner, in step 802, the signal point {haeck over (s)}from the set of signal points S₁ . . . S_(M), which is closest to r isidentified. In this embodiment it is assumed that the constellation ofsignal points corresponds to the constellation of FIG. 7. In FIG. 7,each signal point corresponds to a decision region where the decisionregions are separated by a set of decision boundaries 701 through 706.Hence, the closest signal point {haeck over (s)} may be found byperforming two comparisons of the inphase component and the quadraturecomponent, respectively. For example, if Re(r)<0 (decision boundary 705)and Re(r)<−2d (decision boundary 706) and if lm(r)>0 (decision boundary702) and lm(r)>2d (decision boundary 701), the received signal lies inthe decision region corresponding to S₁, i.e. {haeck over (s)}=S₁ is theclosest signal point. Subsequently, for each bit positions m=1, . . .,log₂(16)=1, . . . ,4, the soft value L_(m) may be calculated using theapproximation of eqn. (7), assuming proper scaling. Consequently, inthis example the soft value L₁ for the first bit isL ₁(S ₁)=K(|−a+jb−(d+3jd)|² −|−a+jb−(−3d+3jd)|²)=K(8ad−8d ²),

Hence, in the above equation, instead of computing two distancessquared, each involving a calculation of the type |x+jy|², the softvalue may be calculated by scaling the inphase amplitude a of thereceived symbol with 8dK and, subsequently, by adding a constant −8 Kd².It is further noted that the constant d may be chosen as any suitablepositive real number.

The remaining three soft values for a received signal in the decisionregion corresponding to S₁ are accordingly:L ₂(S ₁)=K(|−a+jb−(−3d+3jd)|² −|−a+jb−(−3d−jd)|²)=K(−8bd+8d ²)L ₃(S ₁)=K(|−a+jb−(−d+3jd)|² −|−a+jb−(−3d+3jd)|²)=K(4ad−8d ²)L ₄(S₁)=K(|−a+jb−(−3d+3jd)|² −|−a+jb−(−3d+jd)|²)=K(4bd−8d ²),as in the constellation of FIG. 7 the closest symbols with oppositesecond, third, and fourth bit compared to S₁ are S₉=31 3d−jd, S₂=−d+3jd,and S₅=−3d+jd, respectively.

The table 808 of FIG. 9 illustrates the calculated soft values for alldecision regions corresponding to the symbols S₁, . . . ,S₁₆, and forall bits, m=1, . . . ,4. As can be seen from table 808, all soft valuesmay be calculated by scaling one of the inphase component a orquadtrature component b of the received signal r and subsequently addinga constant. Hence, using the pre-calculated equations of table 808, thesoft values may be calculated in a very efficient way. In oneimplementation, each entry of the look-up table 808 may comprise thescaling factor, the constant to be added and a bit indicating whether itis the inphase component a or the quadtrature component b of thereceived signal r which is to be scaled for a given soft value.Preferably, the table is indexed by the decision region and the bitvalues. It is noted, however, that many of the entries of table 808 areidentical. Consequently, it will be apparent to a skilled person thattable 808 may be stored in a memory efficient manner, e.g. by storing alist of the distinct entries and, in table 808, referring to thecorresponding list members. In general, it is noted that constellationswhich are Gray coded or show another regularity, the redundancy of theentries in table 808 may be utilised to reduce the memory consumption oftable 808.

Referring again to FIG. 8, in steps 804-805 the soft values for theidentified decision region and for all bits are calculated. In step 804,the relation to be calculated, i.e. the scaling factor and the constantto be added, are retrieved from a stored table 808 in memory, e.g. alook-up table as shown in FIG. 9. The retrieved relation is calculatedin step 805 resulting in the soft value for the corresponding bitnumber.

It is noted that the processing load in the receiver may further bedecreased by pre-calculating the relations of table 808 and by storingthe pre-calculated soft values: Assuming that the inphase and thequadrature components of the received signal each are quantised to nbits, the soft values of table 808 may be precalculated and tabulatedfor every different inphase and quadrature value, thereby furtherdecreasing the required calculations, as the scaling and adding of step805 are not necessary in this embodiment. However, such a table ofpre-calculated soft values increases the memory consumption. Above,a=|Re(r)| and b=|lm(r)| were defined as the absolute values of the realand imaginary parts of r, respectively, i.e. without sign information.Hence, a and b, each are represented by n−1 bits. If each of thepre-calculated soft values is to be represented by m bits, the totalmemory consumption of a full table is m 2 ^(n−1) 4 16 bits (for each ofthe 16 decision regions and each of the 4 bits, 2^(n−1) different softvalues are stored, each with a precision of m bits). For example, forn=4, the total memory is 512 m bits. Note, however, that in thisembodiment, the pre-calculated table still needs to be multiplied withthe factor K.

It is noted, that the above memory consumption may be further reduced byutilising the fact that many of the entries of table 808 are identicaland by utilising the symmetry of the constellation of FIG. 7.

It is noted that the invention was described in connection with softvalues defined as a log-likelihood ratio indicating a reliability valuefor the bit values of a received sequence. However, other definitions ofsoft values depending on the distance of the received signal to thesignal points may be used as well.

It is further noted that the signal constellations of FIGS. 2 and 7 aremerely used as examples. The calculation of soft values according to theinvention is not limited to these signal constellations.

Finally, it is noted that the embodiment described in connection withFIGS. 5-6 is particularly well suited for large signal constellations,as it saves memory, whereas the embodiment of FIGS. 8-9 is particularlywell suited for Implementing a medium-size signal constellation, e.g.,16QAM, as it saves computational resources.

1. A method of generating a reliability value from a received multilevelsignal in relation to a number of predetermined signal symbols eachassociated with a corresponding bit sequence including a first bitposition, the soft value being indicative of a reliability value for thefirst bit position, the method comprising: identifying a first one ofthe number of signal symbols as being closest to the received multilevelsignal; estimating the soft value as a function of a first distancebetween the received signal and the first signal symbol and of a seconddistance between the received signal and a second one of the number ofsignal symbols that is closest to the first signal symbol andcorresponds to a different binary value at the first bit position of therespective associated bit sequence than the first signal symbol; andwherein estimating the soft value comprises estimating the seconddistance by a stored third distance between the first signal symbol andthe second signal symbol. 2-3. (canceled)
 4. The method according toclaim 1, wherein the step of estimating the soft value comprises thestep of determining (506, 507) a polynomial function of the firstdistance and the second distance, wherein the polynomial function ismultiplied by a predetermined constant (K).
 5. A The method according toclaim 4, wherein the predetermined constant is selected depending on thenoise distribution of the received multilevel signal.
 6. (canceled)
 7. AThe method according to any one of the claims 1, 4, and 5, wherein thethird distance is stored in a look-up table indexed by the number ofsignal symbols and the bit positions.
 8. The method according to any oneof the claims 1, 4, 5, 31, and 32, wherein the method further comprisesthe step of providing the soft value as an input to a decoder. 9.(canceled)
 10. A The method according to any one of the claims 1, 4, 5,31, and 32, wherein the soft value is calculated as a log-likelihoodratio.
 11. A The method according to any one of the claims 1, 4, 5, 31,and 32, wherein the step of identifying the first signal symbol as beingclosest to the received multilevel signal comprises the step ofidentifying the first signal symbol as being closest to the receivedmultilevel signal with respect to a Euclidean distance measure in asignal space.
 12. The method according to claim 11, wherein the signalspace is related to the complex plane in quadrature amplitudemodulation.
 13. (canceled)
 14. A The method according to any one of theclaims 1, 4, 5, 31, and 32, wherein the number of signal symbols areassociated with the number of bit sequences such that the bit sequencesassociated with all nearest neighbours of each signal symbol only differfrom the bit sequence of that signal symbol at one bit position.
 15. Adevice for generating a soft value from a received multilevel signal inrelation to a number of predetermined signal symbols each associatedwith a corresponding bit sequence including a first bit position, thesoft value being indicative of a reliability value for the first bitposition, the device comprising processing means adapted to identify afirst one of the number of signal symbols as being closest to thereceived multilevel signal; and estimate the soft value as a function ofa first distance between the received signal and the first signal symboland of a second distance between the received signal and a second one ofthe number of signal symbols, that is closest to the first signal symboland corresponds to a different binary value at the first bit position ofthe respective associated bit sequence than the first signal symbol;storage means adapted to store a third distance between the first signalsymbol and the second signal symbol; and wherein the processing means isfurther adapted to estimate the second distance by the stored thirddistance. 16-17. (canceled)
 18. The device according to claim 15,wherein the processing means is further adapted to determine apolynomial function of the first distance and the second distance,wherein the polynomial function is multiplied by a predeterminedconstant (K).
 19. The device according to claim 18, wherein thepredetermined constant is a function of the noise distribution of thereceived multilevel signal.
 20. (canceled)
 21. The device according toany one of the claims 15 through 20, wherein the storage means isadapted to store the third distance in a look-up table indexed by thenumber of signal symbols and the bit positions. 22-30. (canceled)
 31. Amethod of generating a soft value from a received multilevel signal inrelation to a number of predetermined signal symbols each associatedwith a corresponding bit sequence including a first bit position, thesoft value being indicative of a reliability value for the first bitposition, the method comprising: identifying a first one of the numberof signal symbols as being closest to the received multilevel signal;estimating the soft value as a function of a first distance between thereceived signal and the first signal symbol and of a second distancebetween the received signal and a second one of the number of signalsymbols that is closest to the first signal symbol and corresponds to adifferent binary value at the first bit position of the respectiveassociated bit sequence than the first signal symbol; and whereinestimating the soft value further comprises the step of selecting,dependent on the first signal symbol and the first bit position, one ofa number of stored functional relations between the received multilevelsignal and the soft value.
 32. The method according to claim 31, whereinthe stored functional relations are stored in a look-up table indexed bythe number of signal symbols and the bit positions.
 33. The methodaccording to any one of claims 1, 4, 5, 31, and 32, wherein identifyingthe first signal symbol comprises comparing the signal components of thereceived multilevel signal with predetermined threshold values.
 34. Adevice for generating a soft value from a received multilevel signal inrelation to a number of predetermined signal symbols each associatedwith a corresponding bit sequence including a first bit position, thesoft value being indicative of a reliability value for the first bitposition, the device comprising: processing means adapted to identify afirst one of the number of signal symbols as being closest to thereceived multilevel signal; and estimate the soft value as a function ofa first distance between the received signal and the first signal symboland of a second distance between the received signal and a second one ofthe number of signal symbols that is closest to the first signal symboland corresponds to a different binary value at the first bit position ofthe respective associated bit sequence than the first signal symbol;storage means adapted to store a number of functional relations betweenthe received multilevel signal and the soft value; and wherein theprocessing means is further adapted to select a functional relation ofsaid number of functional relations dependent on the first signal symboland the first bit position.
 35. The device according to claim 34,wherein the storage means is adapted to store the number of functionalrelations in a look-up table indexed by the number of signal symbols andthe bit positions.
 36. The device according to claim 34, wherein theprocessing means is adapted to identify the first signal symbol bycomparing the signal components of the received multilevel signal withpredetermined threshold values.
 37. The device according to any one ofclaims 34 through 36, wherein the processing means is adapted tocalculate the soft value as a log-likelihood ratio.
 38. The deviceaccording to any one of claims 34 through 36, wherein the processingmeans is further adapted to identify the first signal symbol as beingclosest to the received multilevel signal with respect to a Euclideandistances in a signal space.
 39. The device according to claim 38,wherein the signal space is related to the complex plane in quadratureamplitude modulation.
 40. The device according to any one of claims 34through 36 wherein the number of signal symbols are associated with thenumber of bit sequences such that the bit sequences associated with allnearest neighbours of each signal symbol only differ from the bitsequence of that signal symbol at one bit position.
 41. The deviceaccording to claim 34, wherein the device further comprises a decoderadapted to receive an input signal from the arrangement indicative ofthe determined soft value.
 42. The device according to claim 34, whereinthe device is operable as a mobile terminal.